Dividing machine



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DIVIDING MACHINE Filed Oct. 3, 194:6 15 Sheets-Sheet l ATTORN EY JmL l.yE195@ a. M. DURFEE 4932562 lDIIVIDTNG MACHINE Filed Ooi. 3, 1946 l5Sheets-Sheet 2 BY am? ATTORNEY Jan.. m 195o E. M. DURFEE 2,493,862

DIVIDING MACHINE Filed Oct. 3, 1946 15 Sheets-Sheet 3 ATTQRNEY Jam myE95@ s. M, DURFEE 2,493,862

` DIVIDING MACHINE Filed OGL- 3, 1946 l5 Sheets-Sheet 4 m 559 y u mw mATTORNEY DIVIDING MAGHXNSES Filed Oct.

Jan. 10, 1950, B, M, DURFEE 2,493,862

DIVIDING MACHINE Filed oct.y 5, 1946 15 sheets-sheet s coL.

a 2 a am 5 m2 OLI 05 .L f- BYSIZ M Dur/fee ATTORNEY xNvEN-ro A Jaina ima M. mums-,2E 249393@ DIVIDING MACHINE 15 Sheets-Sheet 7 Filed Ooi). 3,3.946

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DIVIDING MACHINE Filed Oo. 5, 14946 l5 SheecS-Shee 10 .im 10, 195@ E. MDURFEE ,2,493,862

DvIDING MACHINE ATTORN EY" B. M. DURF'EF-Z DVIDING MACHI www l5Sheets-Sheet 14 Filed Ooi. 3, 1946 Jam mi, 3950 a M DURFEE 2,493,862

DIVIDNG MACHINE f Filed Oei. 3, 1946 l Sheets-Sheet l5 o fa c QqcyINVENTOR Beg/'amm M Dur @e ATTORNEY Patented Jan. 10, 1950 DIVIDINGMACHINE Benjamin M. Durfee, Binghamton, N. Y., assignor to InternationalBusiness Machines Corporation, New York, N. Y., a corporation of NewYork Application October 3, 1946, Serial No. 700,877

(Cl. 235-'61l 13 Claims.

This invention relates to improved computing or calculating methods andapparatus for the performance of dividing and square root extractionproblems.

More particularly, it relates to improvements in the operation andcircuit arrangement of an electromechanical rel-ay type of computingmechanism, whereby the assemblage of relatively simple combinations andarrangements of such devices enables the rapid, accurate solution ofmathematical problems.

A specific object of the invention is to provide a dividing appartusbased generally on the overand-over subtraction method of computationmodified to the extent of providing for the subtraction of multiples ofve times the divisor. To this end there is provided a novel registersettable to represent a divisor and provided with a readout device whichselectively reads out either the divisor (in complementary form) ortimes the divisor (in complementary form) in response toa singleelectrical impulse.

In the operation of the apparatus, after representations of the divisorand dividen-d have been set up in separate registers of the relay type,-a third register is automatically set up to represent 5 times thedivisor (in complementary form) with ya 4 set up to the left of thehighest complement digit. A test is then made through an electricalimpulse, to ascertain the relative magnitude ofthe values of thedividend and the multiple set up. If the test indicates a go condition(while the multiple is less than the dividend), subtraction takes placein response to a third electrical impulse to yobtain the remainder andconcurrently, as a result of the tens carry condition, the

entered quotient digit 4 is raised to 5.

Thereafter, the divisor is repeatedly set up in complementary form andcompared with the remainder and each time a go condition is found.. y,

subtraction occurs with accompanying increase of the quotient digit byl. Upon detection of fa no go condition, the quotient digit is set up ina separate register and the remainder is set up asa new dividend with acolumnar shift. 5 times the f edly subtracting from the amount Whoseroot is sought the terms of the series of odd numbers 1, 3, 5, 7, 9,etc. which are the differences between the series of squares l, 4, 9,16, 25, 36, etc. The process commences after the amount is set up byeffecting a setting of the iifth square 25 of the series and testing toascertain if it will go into the highest part of the amount. If it goes,subtraction `occurs and a 5 is set up in ya root register. Thereafter,the odd number 11 corresponding to the next square 36 is set up andcompared with the remainder and, if it goes, the root is increased to 6and the next term 13 corresponding to the next square 49 is tried.

A special arrangement is provided to obtain the successive odd terms byproviding the root register with a novel readout whereby, in response toa single electrical impulse, a reading is obtained of twice the rootamount standing in the register increased by one unit. Thus, a 5 is readout as 11 or 2 times 5 plus 1, and a 6 is read out as 13 or 2 times 6plus 1, etc. When a iina1 root digit for lany denomination is obtained,the next term to be tested will be that required to test for the squareof the root part already obtained with a 5 to the right; that is, if a 6is found to be the first root digit, the next tested for is and the termto be tested is 625. The root register is arranged to obtain this valuein response to a single electrical impulse to read out the root digitwith 25 to the right or times the root plus 25.

Other objects of the invention will be pointed out in the followingdescription and claims and illustrated in the accompanying drawings,which disclose, by way of example, the principle of the invention andthe best mode, which has been contemplated, of applying that principle.

In the :drawings:

Figs. 1a, 1b, 1c 1i arranged vertically in the order named constitute aWiring diagram of the electric circuits of the machine.

Fig. 2 is a, diagram showing the steps involved in the dividingprocedure `f-or the specific problem.

Fig. 3 is la sequence chart showing the order in which Various magnetsare energized for the eX- ample of Fig. 2.

Figs. 4a and 4b constitute a chart showing the steps involved in theextraction of the square root fora specific example.

Fig. 5 is a sequence chart showing the order in which the severalmagnets are energized in carrying out the square root extractionproblem.

Fig. 6 is a timing chart of the several cam controlled contacts of themachine.

3 Division Referring to Fig. 2, a general explanation will first begiven to point out the various steps involved in the procedure ofdividing.

The problem involved is 16376 divided by 356 to obtain a quotient 46.Six registers are involved with columnar or denominational capacities asindicated by numerals at the head of the several register columns. Theseregisters are of the relay type with ve relay magnets per columnarorder, wherein values are entered in accordance with the so-calledquinary system of numeration. In order to simplify the disclosure, thedivisor and dividend amounts will be entered or set up manually.Specifically, the dividened 16376 is set up in the first ve columns ofregister I2, and the divisor 356 is set up as a `9s complement in thethree highest columns of register 9 with the remainder-order of theregister set up with the complement of 0, which is 9 as in- .dicated onthe line designated manual set up.

After this has been done, the further operations proceed automatically,and the rst step in the procedure isto enter the complement of5 timesthe vdivisor into register II. Thisentry is effected under control ofthe setting in register 9, through a special wiring arrangement, wherebythe coinplement of 5 times the divisor which is 8219 is entered' incolumns 2 to 5. Concurrently thereywith, a9 is entered in column I and a4 is entered in column`6. This entry is represented along line 5 of Fig.2.

In the next step of the procedure, a test or comparison is made betweenthe settings in registers I I and I2, which determines whether 5 timesthe divisor is less than the dividend. For the 'present example, thetest results in what will hereinafter be termed a no go indicationsignifying that 5 times the divisor will not go into the dividend. As aresult of this comparison,

register I I willbe reset and, as indicated on line 9, the 9s complementof 1 times the divisor (643) is entered into register II `with 9s alsoentered in columns I and 5. The test is again made as indicated on lineI0, and this time the result of the comparison indicates that thedivisor will go into the dividend. A so-called cross add operation isthen brought about, wherein the amount. standing in register I2 is addedto that in register I I plus a fugitive 1 and entered into register asthe value 112816. The registers I I and l2 are interwired to constitutea so-called cross adding device, whereby when an amount is set up ineach the sum thereof may be read out and entered in another register.

For purposes of the present invention, this cross add device is providedwith a fugitive 1 arrangement whereby, for each cross adding operationduring the dividing process, the value in the lowest order or column "Iofthe receiving register IG is increasedby l, so that the amount now'standing in'register I5 represents the sum'of the :amountsin registersI I and I 2 plusthe fugitive 1.

In the next step (line II), register I2 is reset .and thereafter theamount in register I6 is transferred to register I2 as the new dividend,following which register I6 is reset as indicated along line I3. Thetest kOperation now repeats as a go indication, so that the cross addingoperation is repeated to enter the amount 209256 in register I B. Thisamount is then transferred back to .register 4I2 after the previoussetting has been canceled and a further test is made with another go"condition. so that cross adding repeats forthe third time to obtain Vtheamount 305696 til as indicated on line I8. Again transferring takesplace back to register I2, and the fourth test results in the amount402136 in register I6 as indicated on line 22. Then this amount istransferred back to register I2 and register I6 is reset.

It will be noted that for each cross adding operation the digit incolumns 6 'of registers I2 v'and I6 yis-progressively increased oneunit, so

that this column progressively represents the quotient digit.

As indicated along line 26, the result of the next test indicates a nogo condition, and as a result the `amount in register I2 is now directlyVtransferred to register I8, following which both registers I I and I2are reset. Thereafter, as indicated on lineZS, the amount standing incolrumnsfI-E in-register IS is transferred back to register' I2 with acolumnar shift one place to the left. Concurrently, the quotient digitin column 6 of the register I8 is transferred to col- -umnl 2 Vofregister Il, wherein it remains stored Las one ofthe quotient digits.

lAs-indicated on line v29, the complement of 5 times the divisor is nowagain entered in register Y! I ,and the result' ofthe test indicatesthat there is a go'condition, yso that cross ladding takes `.place withthe sum of 503560 entered in register i I6, which is transferred toregister I2 after registersII and I2 have been reset.

Thereafter, as indicated on line 33, the complement of l times thedivisor is 'entered in register II-and register'IS is reset. Subsequenttest -results'in a go condition and a cross addition to enter the amount600000 into register I6, which amount transfers back to register I2, andupon kthe next test a no go condition is signified to transfer theamount 600000 directly to register I8. Followingthis, the value incolumns I-5 of register I-8 is transferred to register I2 with theIrcolumn shift to the left,r and the digit 5 -in column 6 of register I8is transferred to the rstcolumn in register I'I, so that the quotient-46 ofthe two'factors is now standing in register AIl.

In the physical operation of the machine, each f the lines of Fig. 2represents an electrical im- -pulse period so that, after the dividendand divisor'have been manually set up in registers 9 and I2, thequotient 46 will have been obtained in register I1 after forty impulseperiods, the first of which is arbitrarily designated as the 5 impulse.

y.Examination of the diagram in Fig. 2 indicates that the calculationproceeds on what may ce termed -a four impulse basis, that is, with atest occurring every fourth impulse, and that at each test period one offour different conditions may obtain. These four conditions may be-tabulated -as follows:

A. Go condition with 1 times the-divisor in register II;

B. Go condition with 5 times the divisor in register'I I;

C. NoGo condition `with 1 times the divisor in register II;

`D. "fNo Go condition with 5 times the'divisor in register II.

These Vfour conditionsare exemplified, respectively, at lines I0, 30, 26and 6, and for each condition the suceeding reset, transfer and entryoperations Will vary as summarized in the following:

For condition A Cross add into register I6'.

. Reset register I2.

. Transfer from register I6 to register I2. Reset register I6.

For condition B Cross add into register I6.

. Reset registers II and I2.

. Transfer from register I6 to register I2.

. Enter l times the divisor into register II and reset register I6.

F011 condition C Transfer from register I 2 to register I8.

. Reset registers II and I2.

. Transfer columns I5 of register I8 to register I2 with column shift,and transfer column 6 of register I8 to register I'I.

4. Enter the complement of 5 times the divisor into register I I andreset register I8.

For condition D No cross adding operation takes place.

. Reset register II.

. Idle operation,

. Enter 1 times the divisor into register I I and reset register I6.

The specific manner in which the foregoing operations are carried out bythe mechanism will now be explained with reference to the circuitdiagram. In the circuit diagram (Figs. la to li) the various magnets andtheir related contacts are arranged to minimize the number of crosscircuit connections by arranging the contacts in close association withthe circuits which they control and indicating the related relay magnetsadjacent thereto with suitable identifying designations.

In the circuit diagram the register magnets or relays will be given thecommon designation RG, and these will be suitably grouped and identiedas related to particular registers. Switch SW (Fig. la) is first closedto place current on main lines I2 and I4.

Manual entry of the dividend in register 12.-- Referring to Fig. 1f,register I2 is represented as comprising six columns of magnets RG, Ineach column, the magnets are designated 1, 2, 3, 4 and 5 to representdigital values in accordance with the quinary system of numeration, i.e. the digit values 1, 2, 3 and 4 are represented by energization ofcorrespondingly numbered magnets RG, and the digits 6 to 9 arerepresented by energization of a 5 magnet RG and an oppropriate one terI2 are closed manually, the contacts associated with the 5 and I magnetsin column 4, the contacts associated with the 3 magnetin column 3,"thecontacts associated with the 5 and 2 magnets in column 2 and thecontacts associated with the 5 and I magnets in column I are closedmomentarily, so that the magnets RG in register I2 will be energized torepresent the value 16376. Each magnet RG will close a pair of holdingcontacts designated a, which for those magnets ene'rgized will completea holding circuit from line I2, through the second or holding winding ofthe magnet, its a contacts and common wire I5 to b contacts of resetmagnet REIZ and line I4.

Manual entry of the divisor in register 9.-In a. like manner keycontacts I0 associated with register 9A (Fig. 1f) are operated in the 4columns of this register in accordance with the 9s complement ofthedivisor, that is, these key contacts arer closed to set up the value 643in the three highest orders, and with a 9 in the iirst or lowest orderfor the example chosen which will result in energization of theappropriate magnets RG of register 9, and these will close their holdingcontacts a to provide a holding circuit through common wire I6 to lineI4 to hold until the main switch SW is opened.

Start circuits-In the circuit diagram are shown a number of cam operatedcontacts, all of which are designated with the prefix C. The cams forcontrolling these contacts are all mounted on a common shaft which iscaused to rotate continuously through a suitable power source. Thetiming of the contacts controlled by these cams. is shown in Fig. 6 forone revolution, and it will be understood that this is repeated. In thistime chart the cycle is divided into four impulse periods, during whichthe successive operaions explained in connection with Fig. 2 occur.

To commence dividing operations, the dividing start key I1 (Fig. 1a) isoperated to close contacts I8. These are held closed momentarily sothat, when contacts C3 close at the 3 point in a cycle, a circuit iscompleted through these contacts and contacts I`8 to energize the dividecontrol magnet designated DC I, which will close its a contacts toprovide a holding circuit through normally closed a contacts of restartmagnet RST.

In the sequence diagram (Fig. 3), the point at which this magnet DCI isenergized is indicated for a period of holding which is alsorepresented. 'In the diagram it is also indicated that register 9 andregister I2 have the magnets thereof in energized condition at the startof the cycle. It is also indicated that the start contacts I8 may beopened after magnet DCI has been energized.

At the 4 time in the cycle, a. circuit is completed from line I4 (Fig.1b), through cam contacts C33, wire I9, normally closed a contacts of amagnet designated QSC and numbered 3, a contacts of the magnetdesignated QS (also num- .bered 3), b contacts of magnet DCI (nowclosed),

b contacts of the magnet designated DCZ, magnet SDR to line I2. Thismagnet will close its a contacts to provide a holding circuit throughcommon Wire 20 and cam contacts C24 which will hold magnet 5DR energizedfor the period indicated in Fig. 3. Energization of this magnet willprepare circuits for transferring the complement of 5 times the divisorinto register II during the r next or 5 period in the cycle.

Entering the complement of 5 times the divisore-The circuit connectionsinvolved in the transfer to register II are shown in Fig. 1e, whereinthe contacts controlled by magnets RG in register 9 are shown at thebottom of the iigure Where they are designated b, c, d, e. The registermagnets RG ofregister I'I are shown at the top of the gure and near thecenter are shown contacts of magnet 5DR designated b. The registermagnets RG of register 9 are cross hatched in representation of the onesthat are energized at this time for thespecic problem and the RG magnetsof register I I are also cross hatched with their energizing circuitsemphasized to facilitate tracing thereof. With magnet SDR energized. itscontacts b will be closed, together with three additional contactsdesignated c. When cam contacts C26 close at the 5 point of time of thesequence, a circuit is traceable from line I4, contacts C26, wire 2 I,the left hand c contact of mag.- net SDR, wire 22 extending to the bcontacts of the magnet RG in column 4 of register 9.

In the left hand column of this register, the circuit will continuethrough the b contacts of the 5 magnet (now shifted), c contacts ofthe 4magnet, c contacts of the 3 magnet, c contacts of the 2 magnet, ccontacts of the I magnet (now shifted), wire 23, through one of the bcontacts of magnet SDR (now closed), the 3 wire of the group designated24, the 3 magnet RG in column 5 of register II to line I2.

In column 3 of register 9, the circuit extends from Wire 22, through theb contacts of the 5 magnet, the b contacts of the 4 magnet (nowshifted), c contacts of the 3 magnet, c contacts of the 2 magnet, ccontacts of the I magnet, Wire 2S, one of the b contacts of magnet SDR,to the 2 wire of the group 24 associated with column 4 of register I Ito the 2 magnet RG in this group to line I 2.

In column 2 of register 9, the circuit extends through the b contacts ofmagnet 5, b contacts of magnet 4, b contacts of magnet 3 (now shifted),wire 26, one of the b contacts of magnet SDR to the I wire of the group24 associated with column lof register II, the II magnet RG in thisorder to line I2.

A parallel circuit extends at this time from line I4, through contactsC26, wire 2I, the left hand c contact of magnet SDR, wire 21, one of theb contacts of magnet SDR, the 5 wire 24 related to column 5 of registerII, the 5 magnet RG in this order to line I2.

In column 2 of register 9 a further circuit is traceable from wire 22, bcontacts of magnet 5, b contacts of magnet 4, b contacts of magnet 2, econtacts of magnet 3 (now shifted), b contacts of magnet I, wire 28, apair of b contacts of magnet SDR, to the S wire of the group 24 relatedto the column 2 of register II, thence through the S magnet RG in thisorder to line I2.

In column I of register 9, a circuit extends from Wire 22, through bcontacts of magnet 5 (shifted), b contacts of magnet 4 (shifted), wire29, one `of the b contacts of magnet SDR to the 4 Wire of the group 24related to column 2 of register I I to the 4 magnet RG and line I2.

In column I of register 9, a further circuit is completed from wire 22,b contacts ofy magnet 5 (shifted), e contacts of magnet 3, b contacts ofmagnet I, wire 28 of this order, thence through a pair of d contacts ofmagnet SDR to the 5 wire of the group 24 related to column I in registerII to the 5 magnet RG to line I2.

A further circuit is completed at this time from -llne I4', contactsC25, wire 2|, left hand c contact of magnet SDR, right hand c contacts,wire 30, which extends to the 4 wire of the group 24 related to column Iof register II, and thence through the 4 magnet RG to line I2.

Finally, there is a circuit extending from contacts C2G, through wire2l, the left hand c con'- tacts of magnet SDR, thence through thecentral ccontacts, wire 3I, to the 4 magnet RG in co1- umn 6 of registerII and thence to line I2. In this manner the energization of magnet SDRfollowed by closure oi contacts C26 will transmitk impulses through thecontacts of register 9 to energize the magnets RG of register II in ac-8, cordance with the complement of 5 times the divisor in columns 2 to5, an additional 9 in column I and a 4 in column 6. This 4 is apotential quotient digit and column 6 serves as a temporary storagedevice to retain the setting. When the several RG magnets of register IIare energized, they close their a contacts (Fig. le) to provide holdingcircuits through the magnets which extend through a common wire 32 andcam contacts CI49 and b contacts of reset-magnet REI I to line I4.Setting of register 9 to represent any other amount will similarlyresult in energization of RG magnets of register II to represent thecomplement of 5 times the amount with a 9-t0 the right and a 4 to theleft.

Test circuits-In Figs. 1h and 1i the several contacts controlled by theRG magnets of registers II and I2 are shown and suitably identified.These ycontacts are divided into vertical sections with those to theright constituting what may be termed carry determining circuits andthose to the left constituting the cross adding network for summing upthe two amounts set up.

Referring now to Fig. la, the cross add magnet designed CA will beenergized at sequence or period 5, through a circuit traceable from lineI4, contacts C42, wire 33, b contacts of 3 magnet QSC, c contacts ofmagnet DCI (now closed), and magnet CA to line I2. This magnet closesits a contacts to provide a holding circuit through cam contacts C49 sothat it remains energized for the period indicated in Fig. 3. In Fig; 1g(bottom), this magnet closes contacts b so that, when cam contacts C50in series therewith close, a test circuit will be completed through awire 40 (Fig. 1h) to the carry determining contacts of the II and I2registers. If the adding of the amounts in registers II and I2 wouldresult in a tens carry into the highest order, a magnet designated QCI(Fig. 1h) would be energized.

For the example under consideration, this carry condition is not presentso that the closure of contacts C at this time is ineffective and magnetQCI will not be energized. This magnet controls the effectiveness of thecross adding circuits, and these also accordingly will not be effectiveat this time, so that explanation thereof will be deferred until a laterpoint in the solution of the problem.

There is now present a condition identified as condition D referred tohereinabove, wherein the complement of 5 times the divisor stands inregister II and a no go condition is present, so that there is now tofollow resetting of register II and entry of l times the divisor intosuch register. There will also be an incidental idle resetting operationof register I'B.

Referring to Fig. la, a circuit is completed upon closure of contactsC35 at sequence 6, which is traceable from line I4, contacts C35, dcontacts of magnet DCI (now closed), and magnet DCZ to line I 2. Thismagnet closes its a contacts to provide a holding circuit through acontacts of magnet RST and also through contacts C |60, so that itremains energized from this point along with magnet DCI.

Reset circuits for reqsers 16 and 18.-When contacts C42 close, a circuitis traceable from line I4, contacts C42, wire 33, b contacts of 3 magnetQSC, thence in parallel through e and ,f contacts of magnet DCI (nowclosed), to magnets REIS and REIS to line I2. These two magnets controlresetting of registers I6 and I8 and, since they contain no entries atthis time, this is an idle operation. They close a fntacts' to provideholding circuits through contacts CI58.

Resetting circuits for register 11.-At the 1 sequence time a circuit iscompleted in Fig. 1a from line I4, contacts C52, c contacts of 3 magnetQSC, a contacts of magnet QCI, b contacts of magnet DC2 now closed,magnet REI I to line I2. This magnet closes its a contacts to provide a,holding circuit through contacts C158.

In Fig. le, magnet REII opens its b contacts to break the holdingcircuits of the RG magnets in register II, so that they becomedeenergized upon opening of cam contacts CI49.

Entering the complement of 1 times the divisor in register 11.-At the 1sequence time, a point before register II is cleared, the circuit iscornpleted from line I4 (Fig. la), contacts C52, d contacts of 3 magnetQSC, c contacts of magnet DC2, :u contacts of magnet RG which representsthe value 4 in column 6 of register II (which is now energized) so thatthe circuit continues to magnet IDRC and line I2. This magnet closes itsa contacts to provide a holding circuit through contacts C43, so that itholds for the period indicated in Fig. 3.

Referring to Fig. 1b, at sequence 8 contacts C33 again close and acircuit is traceable from line I4, contacts C33, Wire I9, a contacts of3 magnet QSC, a contacts of 3 magnet QS, d contacts of magnet DC2(closed), a contacts of magnet designated XSI, b contacts of magnetIDRC, to magnet IDR and line I2. Magnet IDR closes its a contacts toprovide a holding circuit through wire and contacts C24.

Referring now to Fig. 1e, magnet IDR closes three sets of b contactsshown in the center of the figure and three additional c contacts at theleft. Now when contacts C26 close at the 9 time, a circuit is completedfrom line I4, through contacts C26, wire 2l, c contacts of magnet IDR towire 35, from which it extends in column 4 of register 9, through the dcontacts in the 5 and I positions, through b contacts of magnet IDR tothe 5 and I wires 24 associated with column 4 of register II, thencethrough the 5 and I magnets RG in this column to line I2, to therebyenter a 6. A parallel circuit extends from wire 35, the d contacts ofcolumn 3 of register 9 in position 4, through a pair oi b contacts ofmagnet IDR to the 4 wire 24 related to column 3 of register II toenergize the 4 magnet in this column. Similarly, for column 2 ofregister 9 a circuit extends from wire 35, through the d contactsinposition 3, to a pair of b contacts of magnet IDR tothe 3 wire of thegroup 24 related to column 2 of register I I, thereby energizing the 3magnet RG in this column. In column I of register 9, the contacts d inthe 4 and 5 positions are closed, so that circuits similar to thosealready traced will extend to the 4 and 5 wires of the group 24 relatedto column I in register II to energize the RG magnets 4 and 5 in thiscolumn.

Concurrently, there is a circuit traceable from line I4, throughcontacts C26 and wire 2I which extends through the right hand c contactsof magnet IDR to the two c contacts to the left thereof, and to the 4and 5 wires 24 related to column 5of register II to energize the 4 and 5RGv magnets in this order. In this manner amount 96439 is entered inregister II as indicated in line 9 of Fig. 2.

From Fig. 3 it will be noted that magnet CA was deenergized at the 8point in the cycle, and now at the 9 point when the divisor is beingentered'into register II magnet CA is again ener- 10 gized (Fig. la)when contacts C42 close', through the circuit already traced, which itWill be observed also branches through the e and f contacts of magnet'DC I- to energize the reset magnets RE I6 and REIS which' is again anidle operation.

Comparison test circuit at sequence point .10.--` Referring to Figs. 1hand 1i, there is shown a circuit network controlled by the registermagnets RG of the II and I2 registers arranged in columns and rowsdivided into a right hand section including four columns of magnets,which deter` mine tens carry conditions between orders, and a left handsection which obtains the algebraic sum of the two values set up in thepair of registers. The manner of operation will be apparent byconsidering the specic example chosen for illustration, for which themagnets RG for register I I are set up for the Value 96439, and themagnets for register I2 are set up in accordance with the Value 16376.To facilitate the explanation, the RG magnets involved are cross hatchedand the circuits controlled through the contacts thereof are emphasized.

The magnet CA will have closed its b contacts (Fig. 1g) so that uponclosure of contacts C50 the test circuit will be completed and this istraceable as'follows: from line I4, contacts C50, b contacts of magnetCA, wire 40 (Fig. 1h) to the contacts of the RG magnets in column ororder 5. From here a circuit extends through the contacts of the 4magnet RG of register II, contacts of the I magnet RG of register I2, apair of contacts of the 5 magnet of register II (shifted), contacts ofthe 5 magnet of register I2 (normal), wire 4I, g contacts of magnet DCIclosed, relay magnet QCI to line I2. The circuit also branches to carrymagnet C related to column 6. Briefly, then, the setting of a 9 incolumn 5 of register I I and the setting of a l in the same column ofregister I2 call for a tens carry and effect the establishment of thecircuit traced to energize the test magnet QCI, which will control theoperation of the cross adding circuits.

Magnet QCI shifts a pair of contacts d in Fig. 1d (bottom) to complete acircuit from line I4, contacts C26, d contacts of magnet QCI, and magnetQ02 to line I2. Magnet QC2 holds through its e contacts and contactsC43. This magnet closes a pair of a, contacts (bottom of Fig. 1g), sothat when contacts C52 close cross adding circuits will be completed.

Before tracing the circuits involved, a brief explanation will be madeof the general arrangement, which is similar to that shown and describedin copending application Serial No. 636,- 526, filed December 21, 1945,now Patent No. 2,490,362.

In order to explain the principle of operation of the cross addingcircuits for one denominational order, the contacts set up by theregister magnets RG are separated into groups enclosed in rectanglesdesignated A, B, C, D (Fig. 1i), column I. In section A are contacts setto represent digits 1 to 4 of both registers and, whenever the sum oithe two digits represents 5, a circuit is completed through this sectionfrom wire 40, to energize a magnet designated A5 in the samedenominational order. A circuit will-also be completed through section Awhenever the sum of the digits set therein totals 6, 7 or 8. Thus, relayA5 will also be energized by a circuit through section A whenever thesum of the digits is 5-8 inclusive. In section C are contacts set up torepresent a 5 entry in each of the two registers. vIf one of the digitsrepresented in this sec-

